If the following pair of equations has infini | vedclass

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(B) The given equations are:$5x + 2y - k = 0$  .......... $(1)$$10x + 4y - 3 = 0$ .......... $(2)$Comparing these with the general form $a_1x + b_1y +

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$\frac{3}{2}$

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(B) The given equations are:$5x + 2y - k = 0$  .......... $(1)$$10x + 4y - 3 = 0$ .......... $(2)$Comparing these with the general form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:$a_1 = 5, b_1 = 2, c_1 = -k$$a_2 = 10, b_2 = 4, c_2 = -3$For a pair of linear equations to have infinite solutions,the condition is:$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$Substituting the values:$\frac{5}{10} = \frac{2}{4} = \frac{-k}{-3}$$\frac{1}{2} = \frac{1}{2} = \frac{k}{3}$Taking the equality $\frac{1}{2} = \frac{k}{3}$,we get:$k = \frac{3}{2}$Thus,for $k = \frac{3}{2}$,the system has infinite solutions.

If the following pair of equations has infinite solutions,then find the value of $k$:
$5x + 2y = k$
$10x + 4y = 3$

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If the following pair of equations has infinite solutions,then find the value of $k$:$5x + 2y = k$$10x + 4y = 3$